CN113348385A

CN113348385A - AVO imaging conditions in elastic wave reverse time migration

Info

Publication number: CN113348385A
Application number: CN202080010500.7A
Authority: CN
Inventors: 赵杨; 张厚竹; 刘红伟
Original assignee: Saudi Arabian Oil Co
Current assignee: Saudi Arabian Oil Co
Priority date: 2019-01-22
Filing date: 2020-01-17
Publication date: 2021-09-03
Also published as: EP3914937A1; SA521422579B1; US11086036B2; US20200233112A1; WO2020154185A1

Abstract

In a general embodiment, a system, apparatus and method of AVO for imaging conditions in ERTM, comprising: the described system provides for efficient and accurate vector wavefield decomposition with corresponding modified dot-product imaging conditions for ERTM derived by using a modified AVO algorithm. In some embodiments, a 1/ω 2 filter is used to modify the phase of the source wavelet and the multi-component recordings and α 2 and β 2 are used to scale the amplitude of the extrapolated wavefield, where ω, α, and β are the angular frequency, local P-wave velocity, and local S-wave velocity, respectively. The result is the correct phase, amplitude and physical units for the separated P-type and S-type wavefields. A divergence operator and a rotation operator may then be applied to the phase corrected and amplitude scaled elastic wavefield to extract a vector P wavefield and a vector S wavefield. With the separated vector wavefields, modified dot-product imaging conditions can be used to produce PP and PS reflectance images.

Description

AVO imaging conditions in elastic wave reverse time migration

Priority requirement

This application claims priority from U.S. patent application No.16/254,227, filed on 22/1/2019, the entire contents of which are incorporated herein by reference.

Technical Field

The present disclosure relates to methods, systems, and devices for improving exploration for hydrocarbons.

Background

In exploration for hydrocarbon reservoirs, the reservoir bed comprises a fine classification of a series of classes of rock and typically has similar lithographic features separated from other rock populations by identifiable boundaries. Furthermore, the lithology of a rock unit includes: a description of a physical property such as color, texture, particle size or composition that is visible at the outcrop, in the hand or core sample, or obtained using optical magnification microscopy. Thus, the identification of the lithology of a reservoir bed is an important aspect of reservoir characterization because the physical and chemical properties of the rock that holds the hydrocarbons or water affect the response of each tool used to measure formation properties. Various lithologies of reservoir intervals are identified for accurate petrophysical calculations of porosity, water saturation, and permeability.

Disclosure of Invention

Embodiments of the present disclosure are generally directed to systems for detecting hydrocarbons by combining extrapolation of source and receiver wavefields with imaging conditions to generate depth images for subsurface wave drag comparison of original seismic facies and transformed seismic facies. The described system provides for marching efficient and accurate vector wavefield decomposition with corresponding modified dot-product imaging conditions of elastic wave inverse time migration (ERTM) by using a modified amplitude versus offset variation (AVO) algorithm.

In one general implementation, a system, apparatus, and method of AVO for imaging conditions in ERTM includes: described inThe system of (1) provides for efficient and accurate vector wavefield decomposition with corresponding modified dot-product imaging conditions of ERTM derived by using a modified AVO algorithm. In some embodiments, 1/ω is used²The filter modifies the phases of the source wavelet and the multi-component recordings and scales the amplitude of the extrapolated wavefield using α 2 and β 2, where ω, α, and β are the angular frequency, the local compressional (P-wave) velocity, and the local shear (S-wave) velocity, respectively. The result is the correct phase, amplitude and physical units for the separated P-type and S-type wavefields. A divergence operator and a rotation operator may then be applied to the phase corrected and amplitude scaled elastic wavefield to extract a vector P wavefield and a vector S wavefield. With the separated vector wavefields, a PP reflectivity image and a PS reflectivity image may be generated using the modified dot product imaging conditions, where PP represents the reflection of the P-wave and PS represents the reflection of the S-wave. PP reflectivity includes a P-wave source side wave field and a receiver side. PS reflectivity includes an S-wave source side wave field as well as a receiver side.

Particular embodiments of the subject matter described in this disclosure can be implemented such that one or more of the following advantages are achieved. The described system can provide accurate separated P-waves and S-waves (both amplitude and phase) from the elastic wavefield. In these examples, the resulting seismic image is of better quality when compared to other methods.

It is to be appreciated that a method according to the present disclosure may include any combination of the aspects and features described in the present disclosure. That is, methods according to the present disclosure are not limited to the combinations of aspects and features specifically described in the present disclosure, but may also include any combination of the aspects and features provided.

The details of one or more embodiments of the disclosure are set forth in the accompanying drawings and the description below. Other features and advantages of the disclosure will be apparent from the description and drawings, and from the claims.

Drawings

Fig. 1A-1D depict results of an ERTM experiment of an example Marmousi model generated according to an embodiment of the present disclosure.

Fig. 2A-2F depict PP and PS images of an example Marmousi model migrated using different elastic wave schemes.

Fig. 3A and 3B depict a comparison of PP reflectivity and PS reflectivity, respectively.

Fig. 4A-4D depict PP data/Z component images (PP/Z component images) of a two-layer model using different fast radiation transfer model (RRTM) schemes.

FIGS. 5A-5D depict PP/Z component images of a two layer model using different elastic wave reverse time imaging or migration (RTM) schemes.

6A-6B depict a comparison of PP and PS reflection coefficients between the peak amplitude of the ERTM image and the analytical solution.

FIG. 7 depicts a flow diagram of an example vector wavefield decomposition process 700 for conducting a seismic survey.

Fig. 8 depicts a block diagram of an example computer system for providing computing functionality associated with algorithms, methods, functions, processes, flows, and processes as described in this disclosure, according to an embodiment.

Detailed Description

The present disclosure generally describes a system for corresponding imaging conditions using an efficient and accurate vector wavefield decomposition method and elastic wave inverse time migration (ERTM). The described system can be used to estimate lithology in formations and image complex structures (e.g., XYZ) to detect hydrocarbons and reduce drilling risk. This disclosure is presented to enable one of ordinary skill in the art to make and use the disclosed subject matter in the context of one or more specific embodiments. Various modifications to the disclosed embodiments will be readily apparent to those skilled in the art, and the general principles defined in this application may be applied to other embodiments and applications without departing from the scope of the present disclosure. Thus, the present disclosure is not intended to be limited to the embodiments shown or described, but is to be accorded the widest scope consistent with the principles and features disclosed herein.

Amplitude Versus Offset (AVO) has become an important technique when detecting hydrocarbons. In AVO analysis, practice may focus on finding more sensitive hydrocarbon indicators and extracting and exploiting anomalies between the seismic and these sensitive parameters. Least squares regression analysis and inversion are common methods in AVO analysis. AVO can detect hydrocarbons because AVO shows a change in the amplitude of the offset, which represents the amplitude of the wave energy as the wave passes through the formation, which is affected by the velocity and density parameters of the overburden so that the density of the formation can be analyzed by analyzing the reflection coefficient. AVO means the change in amplitude with offset caused by the lithology of the fluid.

Furthermore, the formulation of the finite difference solution of the elastic wave equation may be used to model elastic wave propagation among media on a discrete grid. Elastic wave propagation modeling enables the ability to extrapolate the vector wavefield forward and backward in time. One application of such modeling is a depth imaging technique known as Reverse Time Migration (RTM). ERTM combines extrapolation of the source and receiver wavefields with imaging conditions to generate a depth image for subsurface wave impedance contrast of the original seismic facies and the transformed seismic facies.

For example, in contrast to acoustic methods, ERTM may be beneficial for estimating lithology information (e.g., color, texture, particle size or composition) and imaging of certain complex structures (e.g., salt domes, shale rock masses or faults) using both longitudinal (P) waves and transverse (S) waves. For example, the converted shear waves allow/can be used to solve structural and deposition targets in the gas chimney region in Tommeliten oil fields much more accurately than by using longitudinal waves. Furthermore, interpretation of both P-wave and S-wave images shows a greater likelihood of detecting hydrocarbons, for example, in unconventional tight sand reservoirs.

Early attempts at elastic wave imaging were performed in the framework of kirchhoff migration. This method transmits both P-type and S-type reflections into the subsurface along the progression path. Because ray theory has difficulty considering multiple arrivals and computing amplitudes in the caustic region, elastic wave kirchhoff migration is inaccurate and even cannot solve complex structures that exhibit multipath and caustic phenomena. Furthermore, unlike classical ray theory, gaussian beams compute local P-wave and S-wave wavefronts near the central ray by solving for both the moving ray tracing system and the dynamic ray tracing system. In general, gaussian beam migration is a wavefield continuation method that operates on a common offset, common azimuth data volume. The wavefield continuation itself may provide motion correction for the imaging conditions. This migration is similar to kirchhoff migration, but is applicable to local slant stacking using complex-valued travel times and amplitudes. These latter complex quantities come from representing the wavefield as a sum of gaussian beams, which is an approximate solution to the finite frequency ray theory of the wave equation. In some cases, this enables elastic-gaussian beam migration to image complex structures with good robustness and efficiency. However, gaussian beam methods may not be accurate for models with strong velocity variations, since ray tracing is relied upon to construct the central ray.

In contrast, ERTM directly solves the elastic wave equation using multi-component recordings as boundary conditions. Thus, ERTM can be used to reconstruct the forward and backward vector wavefields underground by applying appropriate imaging conditions to produce accurate PP reflectivities and PS reflectivities. In general, when generating a seismic image, the seismic image is typically a zero-lag cross-correlation between the source-side wavefield and the receiver-side wavefield. PP reflectivity includes a P-wave source side wave field and a receiver side. PS represents the P-wave source side wavefield and the S-wave receiver side wavefield. An important step in ERTM is the extraction of longitudinal and transverse modes from the coupled extrapolated wavefield. This helps remove crosstalk artifacts.

One method for achieving waveform separation is to compute scalar potential wavefields and vector potential wavefields by applying a divergence operator and a rotation operator. However, in practice, there are several difficulties when using this method. First, the scalar and vector potential wavefields do not have the same phase, amplitude, and physical units as the extrapolated wavefields. These differences can lead to inaccurate migration results. Second, the three components for a PS image may be difficult to interpret. Third, the wavefield separation method has a polarity inversion problem for PS images. Therefore, without proper correction, the sum of the PS images on the different sources produces a non-structured stacking result.

Instead of using divergence and rotation operators, a vector wavefield decomposition method may be used by solving a system of linear equations in the wavenumber domain. Wavefield decomposition is a technique that decomposes a wavefield into spatially orthogonal eigensolutions of acoustic wave equations in a coordinate system that best fits the geometry of the aperture under consideration. This method produces a vector P wavefield and a vector S wavefield that have the same phase, amplitude, and units as the input elastic wavefield. An equivalent method can also be implemented in the spatial domain, which requires solving the vector poisson equation. Despite the use of faster poisson solvers, the computational cost remains expensive, as is the case for three-dimensional (3D) problems. Another method for performing vector wavefield decomposition is to introduce secondary P-wave equations. The S-wave can be obtained by subtracting the P-wavefield from the coupled total wavefield. While this strategy produces good separation results, solving the secondary P-wave equation also increases computational cost.

In view of the foregoing, the described system provides for efficient and accurate vector wavefield decomposition with corresponding modified dot-product imaging conditions of ERTM derived by using a modified AVO algorithm. In some embodiments, a 1/ω 2 filter is used to modify the phase of the source wavelet and the multi-component recordings and α 2 and β 2 are used to scale the amplitude of the extrapolated wavefield, where ω, α, and β are the angular frequency, local P-wave velocity, and local S-wave velocity, respectively. The result is the correct phase, amplitude and physical units for the separated P-type and S-type wavefields. A divergence operator and a rotation operator may then be applied to the phase corrected and amplitude scaled elastic wavefield to extract a vector P wavefield and a vector S wavefield. With the separated vector wavefields, modified dot-product imaging conditions can be used to produce PP and PS reflectance images. For example, the dot-product imaging conditions are modified by preserving the sign of the dot-product imaging conditions and recalculating the magnitude of the dot-product imaging conditions using a multiplication of the absolute value of the separated source wavefield and the absolute value of the separated receiver wavefield to produce relatively accurate angle-dependent magnitudes. The two-dimensional (2D) numerical example demonstrates the feasibility and robustness of the proposed method. In these embodiments, this imaging condition preserves the sign of the dot product but recalculates the migration amplitude using a multiplication of the absolute value of the separated source wavefield and the absolute value of the separated receiver wavefield. This eliminates the effect of the cosine function cos Δ θ, where Δ θ is the difference in polarization angle between the incident and reflected wavefields. This operation is equivalent to dividing the dot-product imaging result by cos Δ θ.

As an example, in a 2D isotropic elastic medium, the described system may use the linear equation (newton's second law) and the equation of deformation (hooke's law):

wherein v is_x、v_zAre the particle velocity components in the x-direction and z-direction, respectively, of the current travel time t, ρ is the density of the medium, λ is the first lame parameter, and μ is the shear modulus. Sigma_ijRepresenting the ijth component of the symmetric stress tensor.

Substituting equations (3), (4) and (5) into equations (1) and (2) and differentiating time on both sides can be defined according to equations (6) and (7), respectively:

assuming minimal computational cost, equations (6) and (7) can be simplified by assuming a locally constant shear modulus and resulting in the third term being discarded, which can be defined according to equations (8) and (9), respectively:

according to helmholtz' S theory, which can be defined according to equation (10) and equation (11), the sum of the P particle velocity and the S particle velocity is equal to the total particle velocity.

Wherein the content of the first and second substances,

and

the particle velocities of the P-wave in the x-direction and z-direction are indicated, and the same applies to the S-wave. Substituting equations (10) and (11) into equations (8) and (9), the divergence operator from

And

naturally remove S wave, and the rotation operator is responsible for

And

p-wave in (1).

The resulting equation can be rewritten in vector representation for simplicity and defined according to equation (12) and equation (13), respectively:

the constant density, as well as the local P-wave velocity (α) and the local S-wave velocity (β) can be used to represent equations (12) and (13). This can be defined according to equation (14) and equation (15), respectively:

the velocity wavefield v may be represented by a convolution of the green's function g with the source wavelet s. Thus, the angular frequency ω can be approximated in the source term. For example, equation (14) and equation (15) may be approximated as equation (16) and equation (17), respectively:

the input source wavelet and multi-component recording can correspondingly pass through 1/omega²And (6) filtering. In practice to avoid dividing by small frequencies, filtering in the time domain may be achieved using double integration over time for both the source and receiver inputs.

Dot-product imaging conditions for vector-based elastic wave RTM can be used to avoid the problem of polarity inversion of PS images that occurs in conventional elastic wave RTM. However, this imaging condition involves multiplication by a cosine function cos Δ θ, where Δ θ represents the difference in polarization angle between the incident and reflected wavefields. This may lead to an inaccurate estimation of the reflection coefficient. To eliminate the amplitude effect of the cosine function, the dot-product imaging results may be normalized with the absolute value of cos Δ θ. However, when a plurality of waves intersect in a region having a complicated structure, it is difficult to obtain accurate estimation of the propagation direction and the polar direction. To simplify the normalization of the angular dependence, the sign of the dot product can be preserved and the migration amplitude recalculated using multiplication of the absolute value of the separated source wavefield and the absolute value of the separated receiver wavefield. The result is a modified dot-product imaging condition, which may be defined according to equation (18):

and

wherein, I^PPAnd I^PSIs an image for PP reflectivity and an image for PS reflectivity, x_sAnd x is the source and image point location, u is the separated vector wavefield, subscripts S and r denote the source and receiver sides, superscripts P and S denote P-type and S-type, | · | is an absolute value, and T is the recording duration, sgn^PPAnd sgn^PSRespectively for PP imagesNumber and symbol for PS image.

In a first example, a Marmousi model is used to prove the adaptability of the described system to complex structures. The Marmousi model is a complex 2D structural modeling that can be used to compare depth migration and velocity determination models. Such models typically involve horizontal velocity changes and vertical velocity changes.

Fig. 1A-1B depict the results of an ERTM experiment of a first example Marmousi model. FIGS. 1A and 1B depict a true P-wave velocity model and a smoothed P-wave velocity model, respectively. Fig. 1C and 1D depict a true density model and a smoothed density model. The S-wave velocities are constructed by scaling the P-wave velocities by 1.7, respectively. The smoothed model was calculated by applying a triangular filter at 62.5m radius x 62.5m radius.

The P-wave velocity model and the density model are depicted in fig. 1A and 1C. The S-wave velocity model can be constructed by scaling the P-wave velocity by a factor of √ 3. The migration velocity (shown in FIG. 1B) and density (shown in FIG. 1D) can be established by smoothing the true model with a 62.5 meter (m) by 62.5m triangular filter. The 322 seismic sources are deployed uniformly on the surface at equal intervals (e.g., 37.5m intervals). For each shot, a Ricker source with a peak frequency of 20 hertz (Hz) was placed in the middle of the 2500m hole. 400 receivers were used to cover the hole at a 6.25m pitch. The time sample is 0.5 milliseconds (ms) and the recording duration is 4 s.

Fig. 2A-2F depict PP and PS images of a first example Marmousi model migrated using different elastic wave schemes. Fig. 2A and 2B are based on a method of not applying polarity correction to a PS image. Fig. 2C and 2D are calculated using elastic wave field separation based on helmholtz decomposition (method of Zhu). Fig. 2E and 2F use the described system for migration.

Fig. 3A and 3B depict a comparison of PP and PS reflectivity, respectively, at a distance of 2.0 kilometers (km). The PP reflectivity and PS reflectivity are shown as solid lines. The PP reflectivity curve represents true reflectivity. Div and Curl Inverse Monte Carlo (IMC) are based on methods that do not apply polarity correction to PS images. The Markov Decision Process (MDP) IMC, which is the imaging condition of the method of Zhu, is based on the images of the described system. The amplitude is normalized with respect to its maximum value. True reflectivity is calculated using R ═ P v-P0 v 0)/(P v0, where v is the true P-wave velocity or S-wave velocity and v0 is the smoothed P-wave velocity or S-wave velocity, P is the true density and P0 is the smoothed density. PP images based on all three methods have good resolution for complex faults and deep anticlines. But images based on isotropic angular domain elastic wave reverse time migration method have phase shift compared with real PP reflectivity. The amplitude is also overestimated in narrow regions (e.g., from 0km to 1.0km in depth) (see green line in fig. 3A). This is because the divergence and curl operators produce incorrect phase and amplitude during the wavefield decomposition. In contrast, the method of Zhu and the described system are accurate in both phase and amplitude (see red and blue lines of fig. 2A). For PS images, fig. 2B shows the apparent unstructured stacking effect caused by the polarity inversion problem. Using the wavefield decomposition in equation 8 and modified dot-product imaging conditions, the proposed method avoids the polarity inversion problem and produces a clear PS image (fig. 2F). Furthermore, since the influence of cos Δ θ is removed, the PS image amplitude more conforms to the true reflectivity than that of the Zhu-based method (see from 0.2km to 1.0km of fig. 3B).

In a second example, a simple two-layer model is used. The model includes a horizontal reflector set at a depth of 1.6km, for the upper layers, α 2500 meters per second (m/s), β 1443m/s, and ρ 2.0 grams per cubic centimeter (g/cm 3); for the underlayer, α is 3000m/s, β is 1732m/s, and ρ is 2.1g/cm 3. This model was discretized with 601 × 401 grids at 8m spatial intervals. An explosive source with a Ricker wavelet with a peak frequency of 15Hz was deployed at the indicated location. Fig. 4A to 4D and fig. 5A to 5D show PP and PS images using different elastic wave RTM schemes. The images use displacement cross-correlation imaging conditions (DC IMC) to solve for a reflector (reflector) using mixed PP and PS energies (see fig. 4A and 5A). These results have no clear physical significance and are difficult to interpret. Furthermore, this method also produces strong cross-talk artifacts without taking into account the wavefield decomposition. By using divergence operators and rotation operators, the method of isotropic angle domain elastic wave reverse time migration method (called Div and Curl IMC) reduces crosstalk and produces clear PP and PS images (see fig. 4B and 5B). But the divergence and curl operations change the shifted phase and there is a polarity inversion problem for the PS image (see fig. 4B). By applying helmholtz decomposition and dot product imaging conditions, the method of Zhu produces the correct phase and avoids the annoying polarity inversion problems. However, the shifted PP and PS amplitudes are inaccurate, since a cosine function is introduced and therefore cannot be interpreted as a reflection coefficient, especially at large offsets (see dot product lines in fig. 6A and 6B). Within the effective reflection angle, the described ERTM workflow produces as correct a phase as the method of Zhu, producing a more accurate shifted amplitude (see modified dot product lines in FIGS. 6A and 6B).

Fig. 4A-4D depict PP/Z component images of a two-layer model (second example) using different RRTM schemes. Fig. 4A depicts a DC IMC: and (4) scheme. FIG. 4B depicts Div and Curl IMC: and (3) a PP scheme. Fig. 4C depicts the PP protocol for Zhu. Fig. 4D depicts the MDP IMC PP protocol. DC IMC represents a displacement cross-correlation imaging condition. Div and Curl IMC represent isotropic angular domain elastic wave reverse time migration methods that perform wave field decomposition using divergence and rotation operators, and apply scalar potential imaging conditions and vector potential imaging conditions. The method of Zhu performs wavefield decomposition first based on solving the poisson equation, and then applies the dot-product imaging conditions. The MDP IMC represents the described ERTM system, which uses modified dot-product imaging conditions.

Fig. 5A-5D depict PP/Z component images of two layer models using different elastic wave RTM schemes.

Fig. 6A and 6B depict a comparison of pp (a) reflection coefficient and ps (B) reflection coefficient between the analytical solution and the peak amplitude of the ERTM image in fig. 4A-4D and 5A-5D. The resolved PS coefficient line was calculated by solving the Zoeppritz equation. The modified dot product line and the dot product line are image peaks at the reflector using the dot product imaging condition and the modified dot product imaging condition, respectively. Both the dot-product imaging conditions and the modified dot-product imaging conditions produce inaccurate migration amplitudes at offsets above a specified threshold due to insufficient illumination.

FIG. 7 depicts a flow diagram of an example vector wavefield decomposition process 700 for conducting a seismic survey. For clarity of presentation, the following description generally describes method 700 in the context of fig. 1A-6B and 8. However, it should be understood that method 700 may be performed, for example, by any other suitable system, environment, software, and hardware, or combination of systems, environments, software, and hardware. In some embodiments, the various steps of method 700 may be performed in parallel, in combination, in a loop, or in any order.

At 702, a set of seismic data is received for a surveyed subsurface. In some examples, the seismic data set includes a source wavelet and a multi-component record. Next, at step 704, the source wavelet and the multi-component recordings are modified to extrapolate the longitudinal (P) and transverse (S) wavefields. At step 706, the extrapolated P-wavefield and the extrapolated S-wavefield are scaled using the angular frequency, the local P-wave velocity, and the local S-wave velocity to generate a separated vector wavefield. At step 708, dot product imaging conditions are used to generate a PP and PS reflectance images. In some instances, the dot-product imaging condition is modified by preserving a sign of the dot-product imaging condition and recalculating a magnitude of the dot-product imaging condition using multiplication of an absolute value of the separated vector wavefield. Next, at step 710, the production capacity of the surveyed subsurface is evaluated from the generated PP reflectance image and the generated PS reflectance image.

Fig. 8 depicts a block diagram of an example computer system 800 for providing computing functionality associated with algorithms, methods, functions, processes, flows, and processes as described in this disclosure, according to an embodiment. The illustrated computer 802 is intended to include any computing device (e.g., a server, a desktop computer, a laptop or notebook computer, a wireless data port, a smart phone, a Personal Digital Assistant (PDA), a tablet computing device), or one or more processors within such devices (including physical or virtual instances, or both, of the computing device). Additionally, the computer 802 may comprise a computer including an input device (e.g., a keypad, keyboard, touch screen, or other device) that can accept user information and an output device that conveys information associated with the operation of the computer 802, including digital data, visual or audio information (or a combination of information), or a GUI.

The computer 802 can function as a client, a network component, a server, a database, or other persistent or any other component (or combination thereof) of a computer system for executing the subject matter described in this disclosure. The computer 802 is shown communicatively coupled to a network 830. In some implementations, one or more components of the computer 802 can be configured to operate in an environment that includes cloud-based computing, local, global, or a combination of environments.

At a high level, computer 802 is an electronic computing device operable to receive, transmit, process, store, or manage data and information associated with the described subject matter. According to some embodiments, computer 802 may also include or be communicatively coupled to an application server, an email server, a web server, a cache server, a streaming data server, a Business Intelligence (BI) server, or other server (or combination of servers).

The computer 802 may receive requests from a client application (e.g., executing on another computer 802) over the network 830 and respond to the received requests by processing the requests in a software application. Further, requests can also be sent to the computer 802 from internal users (e.g., from a command console or through other access methods), external or third parties, other automation applications, and any other entity, person, system, or computer.

Each of the components of the computer 802 may communicate using a system bus 803. In some implementations, any or all of the components of computer 802 (hardware and/or software (or a combination of hardware and software)) can interact with each other or with interface 804 (or a combination of both) through system bus 803 using Application Programming Interface (API)812 or services layer 813 (or a combination of API 812 and services layer 813). The API 812 may include specifications for routines, data structures, and object classes. API 812 may be independent of or dependent on the computer language, and refers to a complete interface, a single function, or even a set of APIs. Service layer 813 provides software services to computer 802 or other components communicatively coupled to computer 802 (whether shown or not). The functionality of the computer 802 may be accessible to all service consumers using the service layer. Software services (e.g., provided by service layer 813) provide reusable, defined business functions through defined interfaces. For example, the interface may be software written in JAVA, C + +, or other suitable language that provides data in an extensible markup language (XML) format or other suitable format. While shown as an integrated component of computer 802, alternative embodiments may show API 812 or services layer 813 as a separate component relative to other components of computer 802 or communicatively coupled to other components of computer 802 (whether shown or not). Further, any or all portions of the API 812 or the services layer 813 may be implemented as sub-modules or sub-modules of another software module, enterprise application, or hardware module without departing from the scope of the present disclosure.

The computer 802 includes an interface 804. Although illustrated in fig. 8 as a single interface 804, two or more interfaces 804 may be used according to particular needs, desires, or particular implementations of the computer 802. The interface 804 is used by the computer 802 to communicate with other systems (whether shown or not) in a distributed environment that is coupled to a network 830. In general, the interface 804 comprises logic encoded in software or hardware (or a combination of software and hardware) and operable to communicate with a network 830. More specifically, the interface 804 may include software that supports one or more communication protocols associated with communications, such that the network 830 or the interface's hardware is operable to communicate physical signals both inside and outside the illustrated computer 802.

The computer 802 includes a processor 805. Although illustrated in fig. 8 as a single processor 805, two or more processors may be used depending on the particular needs, desires, or particular implementations of the computer 802. In general, the processor 805 executes instructions and manipulates data to perform the operations of the computer 802 and any algorithms, methods, functions, processes, flows, and processes as described in this disclosure.

The computer 802 also includes a memory 806 that retains data for the computer 802 or other components (whether shown or not) that may be connected to the network 830 (or a combination of both). For example, the memory 806 may be a database that stores data consistent with the present disclosure. Although illustrated in fig. 8 as a single memory 806, two or more memories may be used depending on the particular needs, desires, or particular implementations of the computer 802 and the functionality described. While the memory 806 is shown as an integrated component of the computer 802, in alternative embodiments, the memory 806 may be external to the computer 802.

The application 807 is an algorithmic software engine that provides functionality, particularly in relation to the functionality described in this disclosure, according to particular needs, desires, or particular implementations of the computer 802. For example, application 807 may serve as one or more components, modules, or applications. Further, although shown as a single application 807, the application 807 can be implemented as multiple applications 807 on the computer 802. Further, while shown as being integrated with computer 802, in alternative embodiments, application 807 can be external to computer 802.

There may be any number of computers 802 associated with or external to the computer system containing the computers 802, each computer 802 communicating over the network 830. Moreover, the terms "client," "user," and other terms may be used interchangeably without departing from the scope of this disclosure. Moreover, the present disclosure encompasses that many users may use one computer 802, or that one user may use multiple computers 802.

Implementations of the subject matter and the functional operations described in this specification can be implemented in digital electronic circuitry, in tangibly embodied computer software or firmware, in computer hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Embodiments of the subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible, non-transitory computer-readable storage medium for execution by, or to control the operation of, data processing apparatus. Alternatively or additionally, the program instructions may be encoded on an artificially generated propagated signal (e.g., a machine-generated electrical, optical, or electromagnetic signal) that is generated to encode information for transmission to suitable receiver apparatus for execution by data processing apparatus. The computer storage medium may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of computer storage media.

The terms "data processing apparatus," "computer," or "electronic computing device" (or equivalents thereof as understood by those of ordinary skill in the art) refer to data processing hardware and include various devices, apparatus, and machines for processing data. These devices may include, for example, a programmable processor, a computer, or multiple processors or computers. The apparatus may also be or include special purpose logic circuitry, e.g., a Central Processing Unit (CPU), Field Programmable Gate Array (FPGA), or Application Specific Integrated Circuit (ASIC). In some embodiments, the data processing apparatus or dedicated logic circuit (or a combination of the data processing apparatus or dedicated logic circuit) may be hardware-based or software-based (or a combination of hardware-based and software-based). Alternatively, the apparatus may comprise code that creates an execution environment for the computer program, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of execution environments. The present disclosure contemplates the use of data processing devices with or without a conventional operating system (e.g., LINUX, UNIX, WINDOWS, MAC OS, ANDROID, IOS, or any other suitable conventional operating system).

A computer program (which may also be referred to or described as a program, software application, module, software module, script, or code) can be written in any form of programming language, including: a compiled or interpreted language, or a declarative or procedural language, and the computer program may be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. The computer program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network. While the portions of the program shown in the figures are illustrated as individual modules implementing various features and functions through various objects, methods, or other processes, the program may alternatively include multiple sub-modules, third party services, components, or libraries. Rather, the features and functionality of the various components may be combined into a single component.

The processes and logic flows described in this specification can be performed by one or more programmable computers executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., a CPU, FPGA or ASIC.

A computer suitable for executing a computer program may be based on a general purpose or special purpose microprocessor, both, or any other type of CPU. Generally, a CPU will receive instructions and data from a read-only memory (ROM) or a Random Access Memory (RAM) or both. The essential elements of a computer are a CPU for executing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto-optical disks, or optical disks. However, the computer need not have these devices. Further, the computer may be embedded in another device, e.g., a mobile telephone, a Personal Digital Assistant (PDA), a mobile audio or video player, a game player, a Global Positioning System (GPS) receiver, or a portable storage device (e.g., a Universal Serial Bus (USB) flash drive), to name a few.

Computer-readable media (transitory or non-transitory) suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including by way of example: semiconductor memory devices (e.g., erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), and flash memory devices); magnetic disks (e.g., internal hard disks or removable disks); magneto-optical disks; and compact disk read-only memory (CD-ROM), Digital Versatile Disk (DVD) +/-R, DVD-RAM and DVD-ROM disks. The memory may store various objects or data, including: caches, classes, frames, applications, backup data, jobs, web pages, web page templates, database tables, knowledge bases storing dynamic information, and any other information including any parameters, variables, algorithms, instructions, rules, constraints, or references. Further, the memory may include any other suitable data, such as logs, policies, security or access data or reporting files. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.

To provide for interaction with a user, embodiments of the subject matter described in this specification can be implemented on a computer having a display device (e.g., a Cathode Ray Tube (CRT), a Liquid Crystal Display (LCD), a Light Emitting Diode (LED), or a plasma monitor) for displaying information to the user and a keyboard and a pointing device (e.g., a mouse, a trackball, or a trackpad) by which the user can provide input to the computer. Touch screens (e.g., a tablet computer surface with pressure sensitivity, a multi-touch screen using capacitive or electrical sensing, or other types of touch screens) may also be used to provide input to the computer. Other types of devices may also be used to provide for interaction with a user; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user may be received in any form, including acoustic, speech, or tactile input. Further, the computer may interact with the user by sending documents to and receiving documents from the device used by the user; for example, by sending a web page to a web browser on a user client device in response to a request received from the web browser.

The term Graphical User Interface (GUI) may be used in the singular or in the plural to describe one or more graphical user interfaces and each display of a particular graphical user interface. Thus, the GUI may represent any graphical user interface, including but not limited to a web browser, touch screen, or Command Line Interface (CLI) that processes information and efficiently presents the results of the information to the user. In general, the GUI may include a number of User Interface (UI) elements, some or all of which are associated with a web browser, such as interactive fields, drop-down lists, and buttons that are operable by a business suite user. These and other UI elements may be related to or represent functionality of a web browser.

Implementations of the subject matter described in this specification can be implemented in a computing system that includes a back-end component (e.g., as a data server), or that includes a middleware component (e.g., an application server), or that includes a front-end component (e.g., a client computer having a graphical user interface or a web browser through which a user can interact with an implementation of the subject matter described in this specification), or any combination of one or more such back-end, middleware, or front-end components. The components of the system can be interconnected by any form or medium of wired or wireless digital data communication (or combination of data communication), e.g., a communication network. Examples of communication networks include a Local Area Network (LAN), a Radio Access Network (RAN), a Metropolitan Area Network (MAN), a Wide Area Network (WAN), Worldwide Interoperability for Microwave Access (WIMAX), a Wireless Local Area Network (WLAN) using, for example, 802.11a/b/g/n or 802.20 (or a combination of 802.11x and 802.20 or other protocols consistent with this disclosure), all or a portion of the internet, or any other communication system (or combination of communication networks) at one or more locations. The network may transport, for example, Internet Protocol (IP) packets, frame relay frames, Asynchronous Transfer Mode (ATM) cells, voice, video, data, or other suitable information (or combination of communication types) between network addresses.

The computing system may include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.

In some implementations, any or all of the components of the computing system (hardware and/or software (or a combination of hardware and software)) can interact with each other, or interface with each other, using an API or service layer (or a combination of API and service layers). The API may include specifications for routines, data structures, and object classes. An API may be independent or dependent on the computer language and refers to a complete interface, a single function, or even a collection of APIs. The service layer provides software services to the computing system. The functionality of the various components of the computing system may be accessible to all service consumers using the service layer. The software service provides reusable, defined business functions through defined interfaces. For example, the interface may be software written in JAVA, C + +, or other suitable language that provides data in an extensible markup language (XML) format or other suitable format. The API or service layer (or a combination of the API and the service layer) may be an integrated component or a stand-alone component associated with other components of the computing system. Further, any or all portions of the service layer may be implemented as sub-modules or sub-modules of another software module, enterprise application, or hardware module without departing from the scope of the present disclosure.

While this specification contains many specific implementation details, these should not be construed as limitations on the scope of the systems or of what may be claimed, but rather as descriptions of features that may be specific to particular embodiments. Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination.

Specific embodiments of the present subject matter have been described. Other implementations, modifications, and permutations of the described embodiments are apparent to those skilled in the art within the scope of the claims below. Although operations are depicted in the drawings or claims in a particular order, this should not be understood as: it may be desirable to perform the operations in the particular order shown, or in sequential order, or to perform all of the operations shown (some of which may be considered optional) in order to achieve desirable results. In some cases, multitasking or parallel processing (or a combination of multitasking and parallel processing) may be advantageous and may be performed.

Moreover, the separation or integration of various system modules and components in the embodiments described above should not be understood as requiring such separation or integration in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

Accordingly, the above description of example embodiments does not define or constrain this disclosure. Other changes, substitutions, and alterations are also possible without departing from the spirit and scope of this disclosure.

Furthermore, any of the claimed embodiments described below are considered at least applicable: a computer-implemented method; a non-transitory computer-readable medium storing computer-readable instructions for performing a computer-implemented method; and, a computer system comprising a computer memory that is interoperably coupled with a hardware processor configured to execute the computer-implemented method or instructions stored on a non-transitory computer-readable medium.

Claims

1. A computer-implemented method, performed by one or more processors, for varying AVO of amplitude versus offset of imaging conditions in elastic wave reverse time migration ERTM, the method comprising:

receiving a seismic data set of the surveyed subsurface, the seismic data set comprising a source wavelet and a multi-component record;

modifying the source wavelets and the multi-component recordings to extrapolate a longitudinal P wavefield and a transverse S wavefield;

scaling the extrapolated P-wavefield and the extrapolated S-wavefield using the angular frequency, the local P-wave velocity, and the local S-wave velocity to generate a separated vector wavefield;

generating PP and PS reflectivity images using a dot-product imaging condition, wherein the dot-product imaging condition is modified by preserving a sign of the dot-product imaging condition and recalculating a magnitude of the dot-product imaging condition using multiplication of absolute values of the separated vector wavefield; and

evaluating productivity of the surveyed subsurface from the generated PP reflectance image and the generated PS reflectance image.

2. The computer-implemented method of claim 1, wherein modifying the source wavelet and the multi-component record comprises: use of

A filter modifies the phases of the source wavelet and the multi-component record.

3. The computer-implemented method of claim 1, wherein scaling the extrapolated P wavefield and the extrapolated S wavefield comprises: scaling amplitudes of the extrapolated P and S wavefields using the angular frequency, the local P-wave velocity, and the local S-wave velocity to generate a separated vector wavefield.

4. The computer-implemented method of claim 1, wherein the dot-product imaging conditions generate PP and PS reflectance images with substantially accurate angle-dependent amplitudes.

5. The computer-implemented method of claim 1, wherein the dot-product imaging condition uses the following formula:

wherein, I^PPAnd I^PSIs an image for PP reflectivity and an image for PS reflectivity, x_sAnd x is the source and image point location, u is the separated vector wavefield, subscripts S and r denote the source and receiver sides, superscripts P and S denote P-type and S-type, | · | is an absolute value, and T is the recording duration, sgn^PPAnd sgn^PSAre symbols for PP images and symbols for PS images.

6. One or more non-transitory computer-readable storage media coupled to one or more processors and storing instructions that, when executed by the one or more processors, cause the one or more processors to:

7. The computer-readable storage medium of claim 6, wherein modifying the source wavelet and the multi-component record comprises: use of

8. The computer-readable storage medium of claim 6, wherein scaling the extrapolated P wavefield and the extrapolated S wavefield comprises: scaling amplitudes of the extrapolated P and S wavefields using the angular frequency, the local P-wave velocity, and the local S-wave velocity to generate a separated vector wavefield.

9. The computer-readable storage medium of claim 6, wherein the dot-product imaging conditions generate PP and PS reflectance images having substantially accurate angle-dependent amplitudes.

10. The computer-readable storage medium of claim 6, wherein the dot-product imaging conditions use the following formula:

wherein, I^PPAnd I^PSAre images for PP reflectivity and images for PS reflectivity, xs and x are source and image point positions, u is the separated vector wavefield, subscript S and subscript r denote source and receiver sides, superscript P and superscript S denote P-type and S-type, | · | is an absolute value, and T is recording duration, sgn^PPAnd sgn^PSAre symbols for PP images and symbols for PS images.

11. A system, comprising:

one or more processors; and

a computer-readable storage device coupled to the one or more processors and storing instructions that, when executed by the one or more processors, cause the one or more processors to:

12. The system of claim 11, wherein modifying the source wavelet and the multi-component record comprises: use of

13. The system of claim 11, wherein scaling the extrapolated P wavefield and the extrapolated S wavefield comprises: scaling amplitudes of the extrapolated P and S wavefields using the angular frequency, the local P-wave velocity, and the local S-wave velocity to generate a separated vector wavefield.

14. The system of claim 11, wherein the dot-product imaging conditions generate PP and PS reflectance images having substantially accurate angle-dependent amplitudes.

15. The system of claim 11, wherein the dot-product imaging condition uses the following formula:

wherein, I^PPAnd I^PSAre images for PP reflectivity and images for PS reflectivity, xs and x are source and image point positions, u is the separated vector wavefield, subscript S and subscript r denote source and receiver sides, superscript P and superscript S denote P-type and S-type, | · | is an absolute value, and T is recording duration, sgn^PPAnd sgn^PSIs a symbol for PP image and for PS imageThe symbol of (2).